## ch2annex

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**Canonical URL:** [ch2annex](https://www.imf.org/-/media/files/publications/reo/eur/2021/october/english/ch2annex.pdf)

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---

### Methodology overview
- Analysis conducted at quarterly frequency over 2020Q1-Q4; results aggregated to annual 2020 values for chapter figures.
- Start from 2020 real GDP growth outcomes, 푔2020. Pre-pandemic growth trends 푔∗ proxied with October 2019 WEO growth projections.
- First layer: 푔1 ≡ 푔2020 − 푔∗ — output loss due to pandemic.

### Layer 2 — Sectoral composition
- Output losses decomposed to sectoral level:
  - 푔1 = ∑푤푖(푔2020,푖 − 푔푖∗) for 푁 = 10 sectors, where 푤푖 = sector i weight (share in gross value added in 2019) and 푔2020,푖 = sector i growth in 2020.
- Sectoral pre-pandemic trends 푔푖∗ proxied by sectoral growth rate that would give same annual shift in sector shares as observed between 2015–2019:
  - 푔푖∗ = ((푤푖,2019 − 푤푖,2015) / (4푤푖,2019 + 1)) 푔∗
  - 푤푖,2019 and 푤푖,2015 are 2015 and 2019 sector shares.
- Contribution of sectoral composition, 푔2:
  - 푔2 ≡ ∑(푤푖 − 푤̃푖)(푔2020,푖 − 푔푖∗) = 푔1 − ∑푤̃푖(푔2020,푖 − 푔푖∗)
  - 푤̃푖 = PPP-weighted average sectoral weight of European countries (used for counterfactual benchmarking).

### Layer 3 — Within-sector regression contributions
- For each sector i, estimate panel regression over country-time (c,t) for 2020Q1–2020Q4:
  - (푔2020,푖,푐,푡 − 푔푖,푐,푡∗) = 훼푖 + βi푋𝑐 + 훾푖푃𝑐,푡−1 + 휙푖𝑀𝑐,푡 + 휀푖,푐,푡
  - 훼푖 = intercept; 푋𝑐 = vector of pre-pandemic fundamentals (initial conditions from 2019); 푃𝑐,푡−1 = vector of lagged policy variables; 푀𝑐,푡 = vector of contemporaneous mobility variables; 휀푖,푐,푡 = residual.
- Initial conditions standardized so contributions interpreted as differentials from sample average.
- Policy variables lagged to alleviate endogeneity; mobility variables included contemporaneously to capture containment effects.
- Contributions computed by aggregating independent variables times estimated coefficients across sectors:
  - Example: contribution of mobility in quarter t = ∑푤̃푖 휙̂푖 푀𝑐,푡 (counterfactual sector weights 푤̃푖 used).
- Unexplained portion (residual) equals sum of intercept and residuals across sectors using counterfactual weights:
  - ∑푤̃푖(훼푖 + 휀푖,푐,푡)

### Data sources and variable construction (selected)
- Initial conditions and other variables:
  - Trade openness: defined as sum of imports and exports divided by GDP — IMF WEO.
  - Current account balance — IMF WEO.
  - Gini inequality index — WB WDI.
  - Size of shadow economy: as a share of official GDP in 2017 — Medina & Schneider (2018).
  - Median age — UN Population Division, World Population Prospects, 2017 Revision.
  - Hospital beds per 1000 people — OECD, Eurostat, WB WDI, National Authorities.
  - Share of smokers in population: average of male and female smokers ratios — WB WDI.
  - Population density: people per sq. km of land — WB WDI.
- Policy variables:
  - Fiscal support measures: announced measures as percent of 2019 GDP (time variation reflects different vintages of the survey) — IMF COVID-19 Policy Survey.
  - Real interest rates: ex-post real interest rates = key policy rates less CPI inflation, in quarterly averages — Haver Analytics, Eurostat, European Central Bank, National Authorities, IMF staff calculations.
  - Central bank assets: as percent of 2019 GDP — Haver Analytics, European Central Bank, National Authorities.
- Mobility:
  - Stringency of containment measures: quarterly average of higher frequency data — Blavatnik School of Government at the University of Oxford.
  - De facto mobility: quarterly average of residuals from a weekly panel regression with Google mobility (average of mobility indicators for retail and recreation, and workplaces) as dependent variable and stringency and country-quarter fixed effects as independent variables — Google Mobility Reports, IMF staff calculations.

### Sectoral panel regression results — summary highlights
- Regression specification: dependent variable = 2020 real GDP growth net of underlying growth & sectoral composition effects; 164 observations per sector; robust standard errors; significance: *** p<0.01, ** p<0.05, * p<0.1.
- Consistent significant coefficients across multiple sectors (selected example coefficients and signs preserved as in source):
  - Fiscal support measures: positive and significant in many sectors; example coefficients include 0.274***, 0.360***, 0.406***, 0.230***.
  - Stringency of containment: negative and highly significant across virtually all sectors; example coefficients include -0.178***, -0.338***, -0.258***, -0.485***.
  - De facto mobility: positive in several sectors; example coefficient 0.144**.
  - Median age: negative and significant in some sectors; example coefficients include -0.337***, -0.732***, -0.723***.
  - Population density: small negative coefficients in some sectors; example -0.00441***; positive and significant in one sector example 0.0183**.
- Model explanatory power (R-squared) varies by sector: example values include 0.616, 0.594, 0.502.

### Annex 2.2 — Calibration of policy multipliers (fiscal and monetary)
- Fiscal multipliers: average fiscal multiplier 퐹𝑐,푡 computed each quarter by composition:
  - 퐹𝑐,푡 = 푀𝐴𝑇𝐿 푃𝐴𝑇𝐿,푡 + 푀𝐿𝐼𝑄 푃𝐿𝐼𝑄,푡 + 푀𝐵𝑇𝐿 푃𝐵𝑇𝐿,푡
  - 푃𝐴𝑇𝐿, 푃𝐿𝐼𝑄, 푃𝐵𝑇𝐿 are shares of above-the-line, liquidity and below-the-line measures; 푃𝐵𝑇𝐿 = 1 − 푃𝐴𝑇𝐿 − 푃𝐿𝐼𝑄.
- Calibrated multipliers from literature:
  - 푀𝐴𝑇𝐿 = 0.83 (average of multipliers for spending, unconditional transfers, payroll tax cuts and unemployment insurance from Bayer et al. (2020), Faria-e-Castro (2021), Guerrieri et al. (2020)).
  - 푀𝐿𝐼𝑄 = 0.45 (multiplier for liquidity assistance from Faria-e-Castro (2021)).
  - 푀𝐵𝑇𝐿 = 휏 푀𝐿𝐼𝑄 with take-up coefficient 휏 = 1/3.
- Fiscal contribution: for each country, multiply fiscal measures by the average multiplier for the quarter, aggregate four quarters to annual 2020 values.
- Monetary multipliers calibrated separately for:
  - Impact of 1 p.p. cut in policy rate.
  - Impact of increase in central bank assets by 1% of 2019 GDP (captures unconventional monetary policy).
- Multipliers differentiated across countries to reflect transmission (financial depth, etc.); literature used to extrapolate where country-specific estimates unavailable.

### Selected calibrated monetary multipliers (Annex Table 2.2.1 — sample entries)
- Impact of 1 p.p. cut in policy rate (examples):
  - Albania 0.33; Austria 0.42; Belarus 0.33; Belgium 0.42; Croatia 0.33; Czech Republic 0.42; Denmark 0.42; Estonia 0.42; Finland 0.42; France 0.42; Germany 0.42; Hungary 0.33; Ireland 0.42; Israel 0.42; Italy 0.42; Kosovo 0.33; Latvia 0.42; Lithuania 0.42; Netherlands 0.42; Norway 0.42; Poland 0.33; Portugal 0.42; Romania 0.33; Russia 0.14; Spain 0.42; Sweden 0.42; Switzerland 0.42; Turkey 0.75; Ukraine 0.33; United Kingdom 0.43.
- Impact of increase in central bank assets by 1% of 2019 GDP (examples):
  - Albania 0.24; Austria 0.11; Belarus 0.24; Belgium 0.06; Croatia 0.24; Czech Republic 0.24; Denmark 0.08; Estonia 0.33; Finland 0.12; France 0.08; Germany 0.14; Hungary 0.24; Ireland 0.13; Israel 0.04; Italy 0.07; Kosovo 0.24; Latvia 0.18; Lithuania 0.33; Luxembourg 0.15; Netherlands 0.04; Norway 0.10; Poland 0.24; Portugal 0.04; Romania 0.24; Russia 0.24; Spain 0.02; Sweden 0.10; Switzerland 0.01; Turkey 0.24; United Kingdom 0.25.
- Note: calibrated multipliers for increases in central bank assets for several countries are extrapolated from Burriel & Galesi (2018) averages where direct estimates were unavailable.

### Outputs and use
- Calibrated policy contributions = sum of contributions from fiscal policy (using calibrated fiscal multipliers), policy rate cuts, and expansion in central bank balance sheets.
- Annex Figure 2.2.2 shows decomposition of real GDP growth with calibrated policy contributions, alongside underlying growth and sectoral composition (the latter identical to Figure 2.4 in Chapter 2).
- Contributions of mobility and initial conditions (regression-based) are excluded from calibrated-policy decomposition and included in residual.

### Section 2 (bibliographic note)
- Section 2 of the source contains bibliographic references only; it does not include substantive findings, projections, analysis, or policy recommendations.

*Source: ch2annex - Section 1 (Annex 2.1 and Annex 2.2), IMF staff calculations, as provided in the source PDF.*

### Section 1

### Annex 2.1. Decomposition methodology

### Methodology overview
- Analysis conducted at quarterly frequency over 2020Q1-Q4; results aggregated to annual 2020 values for chapter figures.
- Start from 2020 real GDP growth outcomes, 푔2020. Pre-pandemic growth trends 푔∗ proxied with October 2019 WEO growth projections.
- First layer: 푔1 ≡ 푔2020 − 푔∗ — output loss due to pandemic.

### Layer 2 — Sectoral composition
- Output losses decomposed to sectoral level:
  - 푔1 = ∑푤푖(푔2020,푖 − 푔푖∗) for 푁 = 10 sectors, where 푤푖 = sector i weight (share in gross value added in 2019) and 푔2020,푖 = sector i growth in 2020.
- Sectoral pre-pandemic trends 푔푖∗ proxied by sectoral growth rate that would give same annual shift in sector shares as observed between 2015–2019:
  - 푔푖∗ = ((푤푖,2019 − 푤푖,2015) / (4푤푖,2019 + 1)) 푔∗
  - 푤푖,2019 and 푤푖,2015 are 2015 and 2019 sector shares.
- Contribution of sectoral composition, 푔2:
  - 푔2 ≡ ∑(푤푖 − 푤̃푖)(푔2020,푖 − 푔푖∗) = 푔1 − ∑푤̃푖(푔2020,푖 − 푔푖∗)
  - 푤̃푖 = PPP-weighted average sectoral weight of European countries (used for counterfactual benchmarking).

### Layer 3 — Within-sector regression contributions
- For each sector i, estimate panel regression over country-time (c,t) for 2020Q1–2020Q4:
  - (푔2020,푖,푐,푡 − 푔푖,푐,푡∗) = 훼푖 + βi푋𝑐 + 훾푖푃𝑐,푡−1 + 휙푖푀𝑐,푡 + 휀푖,푐,푡
  - 훼푖 = intercept; 푋𝑐 = vector of pre-pandemic fundamentals (initial conditions from 2019); 푃𝑐,푡−1 = vector of lagged policy variables; 푀𝑐,푡 = vector of contemporaneous mobility variables; 휀푖,푐,푡 = residual.
- Initial conditions standardized so contributions interpreted as differentials from sample average.
- Policy variables lagged to alleviate endogeneity; mobility variables included contemporaneously to capture containment effects.
- Contributions computed by aggregating independent variables times estimated coefficients across sectors.
  - Example: contribution of mobility in quarter t = ∑푤̃푖 휙̂푖 푀𝑐,푡 (counterfactual sector weights 푤̃푖 used).
- Unexplained portion (residual) equals sum of intercept and residuals across sectors using counterfactual weights:
  - ∑푤̃푖(훼푖 + 휀푖,푐,푡)

### Data sources and variable construction (selected)
- Initial conditions and other variables:
  - Trade openness: defined as sum of imports and exports divided by GDP — IMF WEO.
  - Current account balance — IMF WEO.
  - Gini inequality index — WB WDI.
  - Size of shadow economy: as a share of official GDP in 2017 — Medina & Schneider (2018).
  - Median age — UN Population Division, World Population Prospects, 2017 Revision.
  - Hospital beds per 1000 people — OECD, Eurostat, WB WDI, National Authorities.
  - Share of smokers in population: average of male and female smokers ratios — WB WDI.
  - Population density: people per sq. km of land — WB WDI.
- Policy variables:
  - Fiscal support measures: announced measures as percent of 2019 GDP (time variation reflects different vintages of the survey) — IMF COVID-19 Policy Survey.
  - Real interest rates: ex-post real interest rates = key policy rates less CPI inflation, in quarterly averages — Haver Analytics, Eurostat, European Central Bank, National Authorities, IMF staff calculations.
  - Central bank assets: as percent of 2019 GDP — Haver Analytics, European Central Bank, National Authorities.
- Mobility:
  - Stringency of containment measures: quarterly average of higher frequency data — Blavatnik School of Government at the University of Oxford.
  - De facto mobility: quarterly average of residuals from a weekly panel regression with Google mobility (average of mobility indicators for retail and recreation, and workplaces) as dependent variable and stringency and country-quarter fixed effects as independent variables — Google Mobility Reports, IMF staff calculations.

### Sectoral panel regression results — summary highlights
- Regression specification: dependent variable = 2020 real GDP growth net of underlying growth & sectoral composition effects; 164 observations per sector; robust standard errors; significance: *** p<0.01, ** p<0.05, * p<0.1.
- Consistent significant coefficients across multiple sectors:
  - Fiscal support measures: positive and significant in many sectors; example coefficients include 0.274*** (column (0) demonstration), 0.360*** (column (2) Industry exc. Cons.), 0.406*** (column (4) Wholesale & retail), 0.230*** (column (8) Real estate).
  - Stringency of containment: negative and highly significant across virtually all sectors; example coefficients include -0.178*** (column (0)), -0.338*** (column (4)), -0.258*** (column (8)), -0.485*** (column (10) Arts & other).
  - De facto mobility: positive in several sectors; example coefficient 0.144** (column (0)); sectoral variations and significance levels differ.
  - Median age: negative and significant in some sectors; example -0.337*** (column (0)), -0.732*** (column (2) Industry exc. Cons.), -0.723*** (column (4) Wholesale & retail).
  - Population density: small negative coefficients in some sectors; example -0.00441*** (column (0)); positive and significant in column (10) (0.0183**).
- Model explanatory power (R-squared) varies by sector: examples include 0.616 (column (0)), 0.594 (column (4) Wholesale & retail), 0.502 (column (8) Real estate).

### Annex 2.2 — Calibration of policy multipliers (fiscal and monetary)
- Fiscal multipliers: average fiscal multiplier 퐹𝑐,푡 computed each quarter by composition:
  - 퐹𝑐,푡 = 푀𝐴𝑇𝐿 푃𝐴𝑇𝐿,푡 + 푀𝐿𝐼𝑄 푃𝐿𝐼𝑄,푡 + 푀𝐵𝑇𝐿 푃𝐵𝑇𝐿,푡
  - 푃𝐴𝑇𝐿, 푃𝐿𝐼𝑄, 푃𝐵𝑇𝐿 are shares of above-the-line, liquidity and below-the-line measures; 푃𝐵𝑇𝐿 = 1 − 푃𝐴𝑇𝐿 − 푃𝐿𝐼𝑄.
  - Calibrated multipliers from literature:
    - 푀𝐴𝑇𝐿 = 0.83 (average of multipliers for spending, unconditional transfers, payroll tax cuts and unemployment insurance from Bayer et al. (2020), Faria-e-Castro (2021), Guerrieri et al. (2020)).
    - 푀𝐿𝐼𝑄 = 0.45 (multiplier for liquidity assistance from Faria-e-Castro (2021)).
    - 푀𝐵𝑇𝐿 = 휏 푀𝐿𝐼𝑄 with take-up coefficient 휏 = 1/3.
- Fiscal contribution: for each country, multiply fiscal measures by the average multiplier for the quarter, aggregate four quarters to annual 2020 values.
- Monetary multipliers calibrated separately for:
  - Impact of 1 p.p. cut in policy rate.
  - Impact of increase in central bank assets by 1% of 2019 GDP (captures unconventional monetary policy).
- Multipliers differentiated across countries to reflect transmission (financial depth, etc.); literature used to extrapolate where country-specific estimates unavailable.

### Selected calibrated monetary multipliers (Annex Table 2.2.1 — sample entries)
- Impact of 1 p.p. cut in policy rate (examples):
  - Albania 0.33; Austria 0.42; Belarus 0.33; Belgium 0.42; Croatia 0.33; Czech Republic 0.42; Denmark 0.42; Estonia 0.42; Finland 0.42; France 0.42; Germany 0.42; Hungary 0.33; Ireland 0.42; Israel 0.42; Italy 0.42; Kosovo 0.33; Latvia 0.42; Lithuania 0.42; Netherlands 0.42; Norway 0.42; Poland 0.33; Portugal 0.42; Romania 0.33; Russia 0.14; Spain 0.42; Sweden 0.42; Switzerland 0.42; Turkey 0.75; Ukraine 0.33; United Kingdom 0.43.
- Impact of increase in central bank assets by 1% of 2019 GDP (examples):
  - Albania 0.24; Austria 0.11; Belarus 0.24; Belgium 0.06; Croatia 0.24; Czech Republic 0.24; Denmark 0.08; Estonia 0.33; Finland 0.12; France 0.08; Germany 0.14; Hungary 0.24; Ireland 0.13; Israel 0.04; Italy 0.07; Kosovo 0.24; Latvia 0.18; Lithuania 0.33; Luxembourg 0.15; Netherlands 0.04; Norway 0.10; Poland 0.24; Portugal 0.04; Romania 0.24; Russia 0.24; Spain 0.02; Sweden 0.10; Switzerland 0.01; Turkey 0.24; United Kingdom 0.25.
- Note: calibrated multipliers for increases in central bank assets for several countries are extrapolated from Burriel & Galesi (2018) averages where direct estimates were unavailable.

### Outputs and use
- Calibrated policy contributions = sum of contributions from fiscal policy (using calibrated fiscal multipliers), policy rate cuts, and expansion in central bank balance sheets.
- Annex Figure 2.2.2 shows decomposition of real GDP growth with calibrated policy contributions, alongside underlying growth and sectoral composition (the latter identical to Figure 2.4 in Chapter 2). Contributions of mobility and initial conditions (regression-based) are excluded from calibrated-policy decomposition and included in residual.

*Source: ch2annex - Section 1 (Annex 2.1 and Annex 2.2), IMF staff calculations, as provided in the source PDF.*

### Section 2

### ch2annex - Section 2

### Content summary
- The section contains bibliographic references only; it does not include substantive findings, projections, analysis, or policy recommendations.

*Source: ch2annex - Section 2*

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_Source: https://www.imf.org/-/media/files/publications/reo/eur/2021/october/english/ch2annex.pdf_